The hotel concierge had heard of neither of the museums I intended to visit that day. Not all that surprising, perhaps, until you consider the scale of the institutions in question. One was the Long Museum, a 10,000 square metre private art gallery owned by one of the biggest art collecting couples in China. The other was the Power Station of Art (PSA), Shanghai's first public museum of contemporary art, named for the enormous former industrial building it occupies on the banks of the Huangpu river.

Both were about to celebrate their first birthdays at the time of my visit to Shanghai in September last year and both were eerily quiet. No one likes an overcrowded gallery, of course, but there's definitely something off-putting about being in a museum alone.

The Long Museum and the PSA are part of an extraordinary wave of high profile public and private museum and gallery building taking place not just in Shanghai but across China. The last couple of years in Shanghai alone have seen the relocation of the China Art Museum; the launch of the Yuz Museum; and the relocation of the Shanghai Himalayas Museum (another private institution) to an enormous new space in Pudong. In March, these institutions will be joined by another – larger – branch of the Long Museum, opening in a newly developed area of the city known as the Xuhui Riverside.

Deep pockets, but how deep?

It's a thrilling time for the Chinese museum sector, but it's also an uncertain one. Attendance figures for both the Long Museum and PSA have been disappointing so far. The PSA attracted only 250,000 visitors in 2013, while the picture at the Long Museum is grimmer still. Wang Wei, the museum's chief curator, and her husband, billionaire businessman Liu Yiqian, spend over £1m on running costs annually and paid out around £30m in capital expenses, but welcomed only 50,000 people through their doors last year. The couple have deep pockets, but it's hard to see how such a project is sustainable in the long-term, especially given their soon-to-open second space has set them back a further £30m.

If Wang is worried about the future, she didn't show it. The curator, who had no experience in the sector before taking the helm at the Long Museum, said she is "satisfied with the current operation situation". There are, however, a number of strategies in place to boost attendance figures, including public lecture programmes for adults and children and a range of membership schemes.

Wang is also looking at exploiting commercial potential of her museums, hiring out spaces for events and working with partners – luxury brands, for example – to raise revenue from different sources. She would like to encourage philanthropy too and is considering approaching foundations in the West for funding.

New media means more for artists

As a state-run institution, the PSA is in a more stable position, but deputy director of planning Li Xu had his concerns about how his museum will fare in the future. He attributes the underwhelming visitor numbers to the PSA's out-of-the-way location and poor transport links: "It has to be accessible. No matter how much you love contemporary art, this place has to be easy to get to or else your passion will be washed away."

Li believes the Chinese education system is also a challenge. "Our education department works very hard," he said, but the emphasis schools put on preparing for high school and university entrance exams means that students have little or no time to spend at institutions like the PSA.

Philip Dodd is chair of Made in China, a London-based company that works with governments, brands, media and creative businesses to facilitate engagement between China and Europe. "The [Chinese] education system still has to undergo a really radical transformation," he said. "The museums are part of that radical transformation".

But Dodd also stresses the crucial role that social media is likely to play in the development of the Chinese museum sector. "There are 675 million mobile phones in China, and that's just scratching the surface," he said. "Because the old media has been state-controlled, this new media, which is much more difficult to control, may become a really interesting place for artists to work in, or private museums to work in."

Is this China's museum era?

The sheer scale of social media engagement in China is also indicative of just how different are the contexts in which museums in China and those in the West are operating. Chinese museums are eager to learn and humble enough to learn from the West, said Dodd. "But they have a different strategy: put up the museum, put in the collection and then begin to develop what one might call the audience for that museum."

It's therefore crucial for the Chinese museum sector to find its own solutions to its own particular challenges, rather than just importing ideas from the West. Wang said she is keen to learn from Western institutions, but added: "In China, private museums have their own characteristics and we have our own reality."

How those institutions – both private and state-run – will fare in the coming years is very hard to predict. "China is beginning a system of museum building that took about 130 years to resolve itself in Europe … so part of our problem at the moment is our expectations of China," said Dodd. "I don't think the future's bright, I don't think it's cheap and cheerful; it'll be very complex, it'll be difficult.

"There will be losses, there will be gains, but I do think that for China – and for Asia more generally – this is the museum era."